Integrability features of a new (3+1)-dimensional nonlinear Hirota bilinear model: multiple soliton solutions and a class of lump solutions

Purpose: This paper aims to propose a new (3+1)-dimensional integrable Hirota bilinear equation characterized by five linear partial derivatives and three nonlinear partial derivatives. Design/methodology/approach: The authors formally use the simplified Hirota's method and lump schemes for determining multiple soliton solutions and lump solutions, which are rationally localized in all directions in space. Findings: The Painlevé analysis shows that the compatibility condition for integrability does not die away at the highest resonance level, but integrability characteristics is justified through the Lax sense. Research limitations/implications: Multiple-soliton solutions are explored using the Hirota's bilinear method. The authors also furnish a class of lump solutions using distinct values of the parameters via the positive quadratic function method. Practical implications: The authors also retrieve a bunch of other solutions of distinct structures such as solitonic, periodic solutions and ratio of trigonometric functions solutions. Social implications: This work formally furnishes algorithms for extending integrable equations and for the determination of lump solutions. Originality/value: To the best of the authors’ knowledge, this paper introduces an original work with newly developed Lax-integrable equation and shows new useful findings.